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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var isInfinite = require( '@stdlib/math/base/assert/is-infinite' );
var abs = require( '@stdlib/math/base/special/abs' );
var cos = require( '@stdlib/math/base/special/cos' );
var sin = require( '@stdlib/math/base/special/sin' );
var floor = require( '@stdlib/math/base/special/floor' );
var PI = require( '@stdlib/constants/float64/pi' );
var MAX_INTEGER = require( '@stdlib/constants/float64/max-safe-integer' );
// VARIABLES //
var MAX_INTEGER_P1 = MAX_INTEGER + 1;
// MAIN //
/**
* Computes the value of `cos(πx)`.
*
* ## Notes
*
* - `cos(-x) = cos(x)`
* - `sin(-x) = -sin(x)`
* - `cos(π/2) = 0`
* - `cos(0) = 1`
* - `cos(π) = -1`
*
* @param {number} x - input value
* @returns {number} function value
*
* @example
* var y = cospi( 0.0 );
* // returns 1.0
*
* @example
* var y = cospi( 0.5 );
* // returns 0.0
*
* @example
* var y = cospi( 0.1 );
* // returns ~0.951
*
* @example
* var y = cospi( NaN );
* // returns NaN
*/
function cospi( x ) {
var ax;
var ix;
var rx;
var y;
if ( isnan( x ) ) {
return NaN;
}
if ( isInfinite( x ) ) {
return NaN;
}
ax = abs( x );
if ( ax > MAX_INTEGER_P1 ) {
// Always even integer...
return 1.0;
}
// Argument reduction (reduce to [0,1))...
ix = floor( ax );
rx = ax - ix;
if ( rx === 0.5 ) {
return 0.0;
}
if ( rx < 0.25 ) {
y = cos( PI*rx );
}
else if ( rx < 0.75 ) {
rx = 0.5 - rx;
y = sin( PI*rx ); // recall sin(-x) = -sin(x), thus returned result will be properly signed
}
else {
rx = 1.0 - rx;
y = -cos( PI*rx );
}
// If the integer of `x` is odd, we need to flip the sign...
return ( ix%2 === 1 ) ? -y : y;
}
// EXPORTS //
module.exports = cospi;
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